A music website sold 68 single songs and 40 albums today. The number of single downloads has been increasing by 12 each day. The number of album downloads has been decreasing by 2 each day. If these trends continue, in how many days will the number of single downloads be 5 times the number of album downloads?

Two systems of equations are equivalent if they have they have the same solution/solutions.

The system of linear equations that can be solved from the matrices is given as follows:

Considering that the row [3, -6] is common to matrices Ax and Ay, the matrix A is given as follows:

A = [-5 4; -8 1]

Hence the multiplication of matrices representing the system is given as follows:

[-5 4; -8 1][x; y] = [3; -6]

Applying the multiplication of matrices, the system of equations is given as follows:

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Answer:

They add up to equal 90 degrees.

Answer

3 grams of the medication = 46.296 grains

Explanation

We are asked to convert 3 grams of medication into grains

1 gram = 15.432 grains

3 grams = 3 × 15.432 = 46.296 grains

Hope this Helps!!!3 grams

Answer:

The cost of 2 1/2 pounds of carrots and 3/4 pound of squash is $ 10.25.

Step-by-step explanation:

Since Hauls Vegetable Market sells carrots that cost $ 3.50 per pound, cucumbers that cost $ 0.69 per pound, and squash that cost $ 2 per pound, to determine what will be the cost for 2 1/2 pounds of carrots and 3/4 pound. of squash the following calculation must be performed:

1/2 = 0.5

3/4 = 0.75

Carrots: 3.50 x 2.5 = 8.75

Squash: 2 x 0.75 = 1.50

8.75 + 1.50 = 10.25

Thus, the cost of 2 1/2 pounds of carrots and 3/4 pound of squash is $ 10.25.

The probability that the mean fill is more than 84.8 ounces is 0.39358

From the question, the given parameters about the normal distribution are

Mean value of the set of data = 88.2

Standard deviation value of the set of data = 1.3

The actual data value = 88.2

The z-score of the data value is calculated using the following formula

z = (x - mean value)/standard deviation

Substitute the given parameters in the above equation

z = (88.2 - 87.9)/1.3

Evaluate the difference of 88.2 and 87.9

z = 0.3/1.3

Evaluate the quotient of 0.3 and 1.1

z = 0.23

The probability that the mean fill is more than 88.2 ounces is then calculated as:

P(x > 88.2) = P(z > 0.23)

From the z table of probabilities, we have;

P(x > 88.2) = 0.5910

Hence, the probability that the mean fill is more than 84.8 ounces is 0.5910

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The complete question is;

The polynomial P(x) = 5x²(x − 1)³(x + 9) has degree ____. It has zeros 0, 1, and ____. The zero 0 has multiplicity ____ , and the zero 1 has multiplicity ____

Answer:

A) degree = 6

B) -9 is also a zero of the polynomial

C) 0 has multiplicity of 2

1 has multiplicity of 3

Step-by-step explanation:

A) To find the degree of the polynomial, we will first have to identify each term [term is for example (x - 1)³]. Thus, to find the degree of each term we will add the exponents.

The terms are;

5x², (x - 1)³, (x + 9)

The exponents are, 2, 3 and 1 respectively.

Thus, degree = 2 + 3 + 1 = 6

B) A zero of a polynomial is the value of x that causes the polynomial function to equal 0.

Since 0 and 1 are zeros, looking at the polynomial P(x) = 5x²(x − 1)³(x + 9), we can tell that when the term which when x = 0 makes the polynomial 0 is 5x².

Similarly, the term which when x = 1 makes the polynomial 0 is (x - 1)³

Thus,we are left with the term (x + 9)

So for the polynomial to be zero, (x + 9) = 0

Thus,x = -9

So -9 is a zero of the polynomial

C) The zero 0 is from the term 5x².

Thus,the multiplicity is the highest power of x which is 2.

The zero 1 is from the term (x - 1)³. Thus, the multiplicity is the highest power of x which is 3

Answer: 2.5 ft

Step-by-step explanation:

Ok, we know that the catcher is located in the y-axis.

As you know, the y-axis cuts the x-axis at x = 0, so the catcher is located at x = 0.

To see the heigth of the ball at x = 0 we can see the table, where we can see that when x = 0, f(x) = 2.5 ft

Then the correct option is the second one, 2.5 ft.

Answer:

The answer is  A. 2.5

The first option

Step-by-step explanation:

If we look at the question you'll see this phrase "X represents the horizontal distance the ball travels in feet" and "f(x) represents the height of the ball in feet."

The question is "The pitcher releases the ball at the highest point in the curve, and the catcher is located at the y-axis. According to the table, how high is the ball when it reaches the catcher?" the underlined words are your clue.

When the graph hit zero, its hit its mark "The catcher" it REACHES the catcher.

so, alas, the answer is 2.5 ft

Answer:

1/6

Step-by-step explanation:

A (6,1)

B (12,2)

slope = (2-1)/(12-6)

1/6

Answer:

do the butterfly method if you don't know how to do that comment and I'll show you a screenshot

Answer:

3:25

Step-by-step explanation:

The photo shows how it's solved.

Answer: 3:25

Step-by-step explanation:

Step 1) Convert the decimal number to a fraction by making 0.12 the numerator and 1 the denominator

0.12 = 0.12/1

Step 2) Multiply the numerator and denominator by 100 to eliminate the decimal point.
0.12 x 100

------------ = 12/100
1 x 100

Step 3) Simplify the fraction in the previous step by dividing the numerator and the denominator by the greatest common factor (GCF) of 12 and 100. (The GCF of 12 and 100 is 4.)

12 ÷ 4

---------  = 3/25  

100 ÷ 4

Step 4) Convert the fraction in the previous step to a ratio by replacing the divider line with a colon like this:  

3  

25   =  3:25

Answer:

2(5) + 2√(3^2 + 7^2) = 10 + 2√58 = 25.2

B is the correct answer.

Answer:

C. $7.15

Step-by-step explanation:

3.5(11)= 38.5

2.85(11)= 31.35

38.5-31.35=7.15

Answer:Y, R, B, G

Step-by-step explanation:

Order matters since the ball is being replaced each time. This is all the possible combinations to take 2 balls with replacement, so you can look at the list and see that RR, RB, and RG are listed. The only other combination when choosing a red first would be to pick a yellow, so RY. This is the same pattern for the others also. Look at the list and see what combinations are already listed.

This is the correct answer;

Please leave a Thanks!

It helps!

Answer:

Step-by-step explanation:

parallel angles are equal

3x + 21 = 6x - 60

combine similar terms:

3x - 6x = -60 - 21

-3x = -81

x = 81/3

x = 27

now, plugin the value of x=27 back into the equation to get the angle:

= 3x + 21

= 3(27) + 21

= 102

= 6x - 60

= 6(27) - 60

= 102

as you noticed, both values are equal 102 = 102 because its a parallel angles

so the equation is 3x + 21 = 6x - 60

================================

i am pretty sure its correct.

Step-by-step explanation:

4(x-6)=2

4x-24=2

4x=2+24

4x=28

x=7

Answer:

9-6r

Step-by-step explanation:

9(1−r)+3r

Use the distributive property to multiply 9 by 1−r.

9−9r+3r

Combine −9r and 3r to get −6r.

Answer: 9−6r

Answer:

-6r + 9

Step-by-step explanation:

9( 1 - r ) + 3r

9 - 9r + 3r

9 - 6r

So, the answer is -6r + 9

Answer:In mathematics, the Euclidean distance between two points in Euclidean space is the length of a line segment between the two points

Step-by-step explanation:It can be calculated from the Cartesian coordinates of the points using the Pythagorean theorem, therefore occasionally being called the Pythagorean distance.

Answer:

i) Consecutive interior angles

ii) Supplementary angles

iii) The two oars are parallel by consecutive interior angles theorem

Step-by-step explanation:

i) m∠1  and m∠2 lie between two line and on the same side of the line passing through the two lines. Therefore, they are consecutive interior angles

ii)x = 10

m∠1 = 6x + 18

= 6(10) + 18

= 60 + 18

= 78

m∠2 = 9x + 12

= 9(10) + 12

= 90 + 12

= 102

m∠1 + m∠2 = 72 + 108 = 180

Since m∠1 and m∠2 add to 180, they are supplementary angles.

iii) The two oars are parallel

consecutive interior angle theorem:

If  a transversal cuts through two line and the consecutive interior angles are supplimentary, then the two lines are parallel

Answer:

If both objects started with no charge, they would carry opposite charges of the same magnitude after rubbing.

Step-by-step explanation:

When one insulator is rubbed against another, some electrons on one insulator might travel to the surface of the other insulator. Electrons are neither lost nor created in this process- they are just moved from one surface to the other.

Let the two insulators in this question be denoted as \(A\) and \(B\). Assume that both insulators were initially not charged.

Let \({\rm e}\) denote the fundamental charge. Each electron carries a negative charge of \((-1\; {\rm e})\). Assume that \(n\) electrons are moved from insulator \(A\!\) to insulator \(B\!\):

In other words, the insulator that lost some electrons (which are negatively charged) now carries less negative charge and becomes positively charged. In contrast, the insulator that gained some electrons now carries more negatively charge becomes negatively charged.

The amount of electrons on the two objects combined stays unchanged. Thus, the amount of charge one insulator lost is equal to what the other insulator gained. Therefore, the sign of the charge on the two insulators would be different, but the magnitude (absolute value) of the charge would be equal.

Therefore, the two objects would be oppositely charged, with the magnitude of the charge on them being equal.

Answer:

\(-\frac{1}{2}\)

Step-by-step explanation:

Slope/Gradient = \(\frac{y1-y2}{x1-x2}\)

P = (-8 , 3) (x1, y1)

Q = (-6 , 2) (x2, y2)

Slope = \(\frac{3-2}{-8-(-6)}\) =\(\frac{1}{-8+6}\) = \(\frac{1}{-2}\) = \(-\frac{1}{2}\)

Answer:

-1/2

Step-by-step explanation:

The formula for the slope is (change in y)/(change in x) or Rise/Run.

The change in y for the two points is: 3 --> 2 which is -1

The change in x for the two points is: -8 --> -6 which is +2

If we input these numbers in the slope equation, we end up with -1/2.

Since we cannot simplify -1/2 further, that is our final answer.

Answer:

.5648

Step-by-step explanation:

i am good at math :)

Answer:

= 56 + 0.048

= 56.048

Step-by-step explanation:

560 tenths + 48 thousandths

= 560 × 0.1 + 48 × 0.001

= 56 + 0.048

= 56.048

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The estimated sum of 7 83/84 is 8 to the nearest whole number.

Mixed fractions are fraction that has a whole number attached to an improper fraction. A mixed fraction can be added by first adding the real whole numbers together, then adding their improper fraction counterparts with it.

Also, we can add two mixed fractions together by first converting all the mixed fractions to improper fractions before adding them together.

Using the first process:

= 4 5/12 + 3 8/14

The whole number are 4 and 3, adding those two together, we have:

= 7 (5/12 + 8/14)

The L.C.M of 12 and 14 is 84.

= 7( (7×5)+ (6*8) )  /84

= 7 (35+ 48/84)

= 7 (83/84)

To decimal, we get 7.988. Therefore, the estimated sum of 7 83/84 is 8 to the nearest whole number.

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In the polynomial function, the number of roots of the graph is 3

Polynomial function:

In math, polynomial function refers a function that involves only non-negative integer powers or only positive integer exponents of a variable in an equation like the quadratic equation, cubic equation, etc.

Given,

Here we need to identify the number of roots of the graph.

If we have the graph like the following,

Then to identify the roots, we have to look at the graph start from negative infinity and end at positive infinity.

While we looking into the given graph, we have identified that, the degree of polynomial must be odd.

And in graph, we can see it cuts at three points

=> (-6,0)    (-2,0)    (-1,0)

This are the points on the graph has three x-intercept.

We know that, the number of x-intercept is equivalent to real roots of the polynomial.

Therefore, graph is cubic polynomial because it has three x-intercept.

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Answer:

9

Step-by-step explanation:

5*2=10 28-10=18 18/2=9

uhm when you are sending a question, there will be a button that an attatchment (its name is 'add attachment') press on it and add your picture!

Answer:

the area of the rectangle is A=L•W

The length is 3m less than twice its width W: L+ 3m=2W...->, L=2W-3m

A=L-W

27m²=(2W-3m)-W

27m2=2w2-3m-W

2w2-3wm-27m2=0

....use quadratic formula -(-3m)+ (-3m)²-4-2-(-27m²)

W=

2-2

w=(3m± √9m²+216m²)

w=(3m+ √225m²)

W=(3m± 15m...you need only positive root because width cannot be negative

W= 3m+15m

4

W=. 4

18m

W=4.5m ......now find the L

L=2.4.5m-3m

L=9m-3m

L=6m

Answer:

W = 4.5cm

L = 6cm

Step-by-step explanation:

Answer:

no

Step-by-step explanation:

Answer: No. It isn't equivalent.

Step-by-step explanation: Because 5/7 is not a multiple of 1/2. The multiples of 1/2 are: 2/4, 3/6, 4/8, 5/10 etc.

From conditional statements, there can be built a Tautology.

According to the question, when the Hypothesis is true and the conclusion is false, the result will be false. And that's correct.

But when a conditional statement can a Tautology, given the fact that not always a conditional statement will return the logical value of truth? Look at this example below:

1)James is from Orlando and he lives in Florida. Therefore, James is from Orlando.

2)James is from Orlando and he does not live in Florida. Therefore, James is from Orlando.

3)James is not from Orlando and lives in Florida. Therefore, James is from Orlando.

4)James is not from Orlando and he does not live in Florida. Therefore, James is from Orlando.

What we have above is symbolic for:

p∧q→p

And this is tautological, since no matter, what we have line 2 for p∧q, q being false it does not change the value for false, in any way for the whole proposition p∧q→p. What gives us a Tautology?

This, p∧q→p can be rewritten as p∧q⇒p.

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